Question: Rewrite as a simplified fraction. ${2.2\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 226.6666...\\ 10x &= 22.6666...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 204}$ ${x = \dfrac{204}{90}} $ ${x = \dfrac{34}{15}} \text{or} {2 \dfrac{4}{15}}$